Classical and Quantized Affine Physics: A Step towards it

DOI

10.2991/jnmp.2004.11.s1.21How to use a DOI?

Abstract

The classical and quantum mechanics of systems on Lie groups and their homogeneous spaces are described. The special stress is laid on the dynamics of deformable bodies and the mutual coupling between rotations and deformations. Deformative modes are discretized, i.e., it is assumed that the relevant degrees of freedom are controlled by a finite number of parameters. We concentrate on the situation when the effective configuration space is identical with affine group (affinely-rigid bodies). The special attention is paid to left- and right-invariant geodetic systems, when there is no potetial term and the metric tensor underlying the kinetic energy form is invariant under left or/and right regular translations on the group. The dynamics of elastic vibrations may be encoded in this way in the very form of kinetic energy. Although special attention is paid to invariant geodetic systems, the potential case is also taken into account.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Jan J. Slawianowski
AU  - Vasyl Kovalchuk
PY  - 2004
DA  - 2004/10/01
TI  - Classical and Quantized Affine Physics: A Step towards it
JO  - Journal of Nonlinear Mathematical Physics
SP  - 157
EP  - 166
VL  - 11
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2004.11.s1.21
DO  - 10.2991/jnmp.2004.11.s1.21
ID  - Slawianowski2004
ER  -